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#476 Re: Help Me ! » A few questions » 2013-03-14 14:45:43

Nehushtan
Agnishom wrote:

Please help me with the problem attached

This is what I got.


Let
be the centre of
and
the point of contact of
with
. Let
be the centre of
and
the point of contact of
with
.

Let

be the point on
such that
is a rectangle. Applying Pythagoras’s theorem to
gives
.

Let

be the point on
such that
is a rectangle. Applying Pythagoras’s theorem to
gives
.

Let

be the point on
such that
is a rectangle. Applying Pythagoras’s theorem to
gives
.

Then

Hence:

[align=center]

[/align]

#477 Re: Help Me ! » Thr Circle and Two Parallel Chords » 2013-03-12 14:23:10

Nehushtan

I got

#478 Re: Puzzles and Games » Scientia’s puzzles » 2013-03-11 05:26:20

Nehushtan

#479 Re: Guestbook » money » 2013-03-10 02:12:21

Nehushtan

Rich folks may ride on camels, but it aint’t so easy for ’em to see out of a needle’s eye.

Words of wisdom from Mrs Gamp in Martin Chuzzlewit.

#480 Re: Exercises » Scientia’s exercises » 2013-03-09 09:08:10

Nehushtan

#481 Re: Introductions » Nehushtan » 2013-03-09 05:11:43

Nehushtan

Oh yes, I forgot mathematics. tongue

#482 Re: Introductions » Nehushtan » 2013-03-09 04:11:55

Nehushtan

Thanks for the welcome. smile

Now don’t let my avatar fool you. I’m actually a very gentle creature. I just like to hide beneath a scary mask. big_smile

I believe you have a member called scientia, who has been here for some time now. I’m her partner in real life. We are united by our passion for science, the arts, and Harry Potter. cool

#483 Re: Euler Avenue » Was mathematics invented or discovered? » 2013-03-09 03:18:05

Nehushtan

Well, something was invented if it hadn’t existed before and was brought into existence by human agency; on the other hand it was discovered if it has always existed, even before humans were aware of it.

Thus the natural numbers were discovered. They existed before the first humans were aware of them, and would have continued to exist if there had been no humans to be aware of them. But after discovering them, the humans needed a way to represent them concretely. The Romans came up with I, II, III, …, while the Chinese use 一, 二, 三, …. Our modern notation 1, 2, 3, …, was first used by the Indians – who could thus be said to have invented it. Similarly the arithmetical operation of addition and the relation of equality were discovered, while the symbols + and = were only first used in the 16th century by the Welsh mathematician Robert Recorde – and since he was the first to use them, we say can say that he invented them.

http://z13.invisionfree.com/SAKE/index. … wtopic=267

#484 Euler Avenue » Was mathematics invented or discovered? » 2013-03-09 02:49:22

Nehushtan
Replies: 23

This is a question I’ve seen on at least two other forums. I did a search here but couldn’t find any thread on this topic so I thought I’d start one.

Was mathematics invented or discovered?

My humble opinion is that mathematical truths and ideas were discovered, but the tools and equipment we use to study them were invented. As an example, take this statement: 1 + 2 = 3. My belief is that the truth behind the equation was discovered, but the symbols “1”, “+”, “2”, “=” and “3” were invented.

Any thoughts? smile

#485 Introductions » Nehushtan » 2013-03-09 02:29:56

Nehushtan
Replies: 28

Hi! I’m Nehushtan,
Brazen worshipper of snakes,
Ophiolater.

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